Section 36. Any town which has accepted chapter four hundred and eighty-seven of the acts of nineteen hundred and thirteen, and has a call or part call fire department which now is or may hereafter be subject to chapter thirty-one, may, on the recommendation of the board of engineers of the fire department or of the officer or board having charge of the fire department, promote to membership in the permanent full-time force, without civil service examination and without any probationary period of service required under said chapter thirty-one and the rules and regulations made thereunder, any persons then in the call or part call fire department who have served as call men or part call men or substitute call men for three or more successive years, and who are certified to be competent physically for the duty by the town physician, if any, otherwise by a physician designated therefor by the board of engineers or other authority, as aforesaid; provided, at the time of said promotion to the full-time force, the person so promoted is serving in the call department on a permanent basis after certification from an eligible list established in accordance with the provisions of chapter thirty-one.